arXiv subjects
Publications and source records attributed to Miranda C. N. Cheng.
In this thesis we study the spectra of supersymmetric states in string theory compactifications with eight and sixteen supercharges, with special focus placed on the quantum states of black holes and the phenomenon of wall-crossing in these theories. A self-contained introduction to the relevant background material is included.
The microstates of 4d BPS black holes in IIA string theory compactified on a Calabi-Yau manifold are counted by a (generalized) elliptic genus of a (0,4) conformal field theory. By exploiting a spectral flow that relates states with different charges, and using the Rademacher formula, we find that the elliptic genus has an exact asymptotic expansion in terms of semi-classical saddle-points of the dual supergravity theory. This generalizes the known "Black Hole Farey Tail" of [1] to the case of attractor black holes.
In this note we construct families of asymptotically flat, smooth, horizonless solutions with a large number of non-trivial two-cycles (bubbles) of N=1 five-dimensional supergravity with an arbitrary number of vector multiplets, which may or may not have the charges of a macroscopic black hole and which contain the known bubbling solutions as a sub-family. We do this by lifting various multi-center BPS states of type IIA compactified on Calabi-Yau three-folds and taking the decompactification (M-theory) limit. We also analyse various properties of these solutions, including the conserved charges, the shape, especially the (absence of) throat and closed timelike curves, and relate them to the various properties of the four-dimensional BPS states. We finish by briefly commenting on their degeneracies and their possible relations to the fuzzball proposal of Mathur et al.
We derive necessary conditions for the spinorial Witten-Nester energy to be well-defined for asymptotically locally AdS spacetimes. We find that the conformal boundary should admit a spinor satisfying certain differential conditions and in odd dimensions the boundary metric should be conformally Einstein. We show that these conditions are satisfied by asymptotically AdS spacetimes. The gravitational energy (obtained using the holographic stress energy tensor) and the spinorial energy are equal in even dimensions and differ by a bounded quantity related to the conformal anomaly in odd dimensions.